The survival probability of a weakly subcritical multitype branching process in iid random environment

M Peigné (1) , Thi da Cam Pham (2, 3)

1 IDP - Institut Denis Poisson
2 CERADE ESAIP - ESAIP Centre d’Etudes et de Recherche pour l’Aide à la Décision
3 LAREMA - Laboratoire Angevin de Recherche en Mathématiques

We study the asymptotic behavior of the probability of non extinction of a weakly subcritical multitype branching process in iid random environments. Under suitable assumptions, the survival probability is of order of $\rho^n n ^{-3/2}$ for some $\rho \in (0, 1)$ to specify.

Mots clés: multitype branching process; survival probability; random environment; product of random matrices; weakly subcritical case

Domaines: Probabilités [math.PR]

M Peigné, Thi da Cam Pham. The survival probability of a weakly subcritical multitype branching process in iid random environment. 2023. ⟨hal-03939557v3⟩